I want to point out that this is a whole concept in Sweden. Traditionally, you were supposed to serve at least seven kinds of cookies during the kafferep that was sort of the precursor of the modern day fika.
There is also a book with the same title which is one of the biggest bestsellers of any category in Sweden.
I think that "en kaka" used to be something rather simple (flour, sugar & butter), but nowadays even bigger cakes with for example berries and whipped cream can be called "kaka":
kladdkaka med hallon och vispgrädde
If it has several layers, it's normally called "tårta" though:
None, I think. But it is important to remember that "slag" is an ett-word and "sort" is an en-word. So, it is "ett slags hund" even though "hund" is an en-word. It is a very common mistake, also by Swedes, to say "en slags hund" instead.
By the way, your Swedish is very good! But you are not Swedish, are you?
I can't quite wrap my head around sorter being in genitive here. Can somebody elaborate on why it's not "sju sorter av kakor", which would make more sense? I don't really get why it should be "seven of types cookie". Is this just how this construct works in Swedish and if so, are there more things like this?
It might help to consider the English construction as a possessive: "types OF cookies". It's not quite true but it's essentially the same construction, and that's how Swedish treats it. And Swedish can only phrase possession as "the x's y", not as "the y of x", so we need the other construction for the possessive.
For similar phrasing that isn't possessive, Swedish does use av, med, etc. For instance: sju bitar av tårtan = seven pieces of the cake, where the av denotes pieces of a whole.
Then again, if you use a synonym, you do use the other construction so maybe I'm grasping at straws - I'm honestly not entirely sure. That is: sju typer av kakor.
I think I struggle with the same problem as Kvist. Changing “the y of x” to “the x’s y” wouldn’t give you “sorters kakor” but “kakors sorter”. (e.g. “the Prime Minister of Sweden” becomes “Sveriges statsminister” not “statsministers Sverige”). Is this just how Swedish works in this case, that you have to put the types into the genitive instead of the cookies? And are there more examples than sorters and slags which I found in this thread? Could you also say “Sju bitars tårta” or “Sju typers kakor”?
I can't get used to this flaw of Duolingo: I never actively learned the word 'sorters' on Duolingo. So theoretically I don't know the word at all. But I dó get it as a listen-and-write-down question, which is a little weird from an educational point of view off course...
Interesting that the -rs ending of "sorters" isn't a retroflex sound here. Is that correct? It seems to contradict this source: http://www.glottopedia.org/index.php/Swedish_Phonology#Retroflex_Consonants_2
EDIT: I can hear it in slow speed, so maybe it is less noticeable to me at full speed. Most of the time, in other lessons, it is very pronounced.